×

zbMATH — the first resource for mathematics

Permanence for nonautonomous Lotka-Volterra cooperative systems with delays. (English) Zbl 1186.34119
Summary: We consider a class of nonautonomous two species Lotka-Volterra cooperative population systems with time delays, and establish sufficient conditions which ensure the system to be permanent.

MSC:
34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K25 Asymptotic theory of functional-differential equations
92D25 Population dynamics (general)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Chen, L.; Lu, Z.; Wang, W., The effect of delays on the permanence for lotka – volterra systems, Appl. math. lett., 8, 71-73, (1995) · Zbl 0833.34071
[2] Lin, S.; Lu, Z., Permanence for two-species lotka – volterra systems with delays, Math. bio. eng., 3, 137-144, (2006), (electronic) · Zbl 1089.92059
[3] Lu, G.; Lu, Z., Global stability for \( n\) -species lotka – volterra systems with delay. II. reducible cases, sufficiency, Appl. anal., 74, 253-260, (2000) · Zbl 1016.92028
[4] Lu, G.; Lu, Z., Permanence for two species lotka – volterra cooperative systems with delays, Math. bio. eng., 5, 477-484, (2008) · Zbl 1158.92043
[5] Lu, Z.; Wang, W., Permanence and global attractivity for lotka – volterra difference systems, J. math. bio., 39, 269-282, (1999) · Zbl 0945.92022
[6] Muroya, Y., Uniform persistence for lotka – volterra-type delay differential systems, Nonlinear anal. RWA, 4, 689-710, (2003) · Zbl 1044.34035
[7] Saito, Y., The necessary and sufficient condition for global stability of a lotka – volterra cooperative or competition system with delays, J. math. anal. appl., 268, 109-124, (2002) · Zbl 1012.34072
[8] Xu, R.; Chen, L., Persistence and global stability for a delayed nonautonomous predator – prey system without dominating instantaneous negative feedback, J. math. anal. appl., 262, 50-61, (2001) · Zbl 0997.34070
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.